- The line AB has equation 5x – 2y = 7. The point A has coordinates (1, -1) and the point B has coordinates (3,k). (a) (i) Find the value of k. (ii) Find the gradient of AB. (b) Find an equation for the line through A which is perpendicular to AB. (c) The point C has coordinates (-6, -2). Show that AC has length pV2, stating the value of p. ​

Answers

Answer 1

Step-by-step explanation:

For finding k we'll have to plug in the x-value of the coordinate (3,k) into the equation, and solve for the y:

5(3) - 2y = 7

15 - 2y = 7

2y = 8

y = 4 => k =4

2) I assume the gradient is the slope of the line. If so, just isolate the y in the original equation and see what's the coefficient of the x:

-2y = -5x + 7

y = (5/2)x + 7/2 => the gradient is 5/2

3) the condition of perpendicularity is expressed by the following relation:

a * a' = -1

Where a is the slope of the first line and a' of the second line. We need to find a' that will be:

-1/a = -1/(5/2) = -2/5

The perpendicular line will be:

y = (-2/5)x + b

We need to find  b, and we know that this line passes through A (1,-1):

-1 = (-2/5)*1 + b

b = -1+(2/5) = -3/5

The equation will be:

y = (-2/5)x - 3/5.

4) I don't know what that symbol means (pV2).


Related Questions

LAST ATTEMPT MARKING AS BRAINLIEST!! (Pythagorean theorem )

Answers

10 km is the answer
Your welcome

a certain pharmaceutical company know that, on average 4% of a certain type of pill has an ingredient that is below the minimum strength and thus unacceptable. what is the probability that fewer that 5 in a sample of 20 pills will be acceptable?

Answers

Using the binomial distribution, it is found that there is a 0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

For each pill, there are only two possible outcomes, either it is acceptable, or it is not. The probability of a pill being acceptable is independent of any other pill, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.

In this problem:

The sample has 20 pills, hence [tex]n = 20[/tex].100 - 4 = 96% are acceptable, hence [tex]p = 0.96[/tex]

The probability that fewer that 5 in a sample of 20 pills will be acceptable is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.96)^{0}.(0.04)^{20} = 0[/tex]

[tex]P(X = 1) = C_{20,1}.(0.96)^{1}.(0.04)^{19} = 0[/tex]

[tex]P(X = 2) = C_{20,2}.(0.96)^{2}.(0.04)^{18} = 0[/tex]

[tex]P(X = 3) = C_{20,3}.(0.96)^{3}.(0.04)^{17} = 0[/tex]

[tex]P(X = 4) = C_{20,4}.(0.96)^{4}.(0.04)^{16} = 0[/tex]

0% probability that fewer that 5 in a sample of 20 pills will be acceptable.

A similar problem is given at https://brainly.com/question/24863377

Oceanside Bike Rental Shop charges 13 dollars plus 8 dollars an hour for renting a bike. Tim paid 45 dollars to rent a bike. How many hours did he pay to have the bike checked out?​

Answers

Step-by-step explanation:

Shop charges =13

Many left for renting bike = 45-13 =$32

If renting for 1hr cost $8

then renting for X Hrs will cost $32

1/X =8/32 cross multiplying

8X= 32

X= 32÷8= 4hrs

Factorize the expressions
px2 + qx

Answers

Answer:

SOLUTION

HERE,

=X(P.2+Q)

=X(2P+Q)

Answer:

x(px+q) ( I took x as a common and the remaining are some

The owner of a small store buys coats for 55.00 each

He sells the coats for 66.00 each

Answers

he must buy 24 jackets to get atheist 260 dollars

Find the value of a
I’m decided go between 40 and 6.4

Answers

a = 10
Since the triangles are similar, you can set up a proportion using the corresponding sides and solve.
(16/8 = 20/a)
Hope this helps!

How much does Bethany spend in week 4?

Answers

The sum of known =179
The unknown = x
179+x/6=39
179+x =39*6
x = 234-179

write an equivalent expression for 3(2z+4)

Answers

The answer is : 6z+12

Answer:

6z+12

Step-by-step explanation:

you distribute it

John Marlow's total income last year was $31,300. Of that amount, he spent
$7,900 for food. What percent of Jon's total income did he spend for food? *
25%
40%
50%
85%

Answers

Based on the information given the  percent of Jon's total income did he spend for food is 25%.

Using this formula

Percent of total income=Amount spent for food/Total income last year

Where:

Amount spent for food=$7,900

Total income last year=$31,300

Let plug in the formula

Percent of total income=$7,900/$31,300

Percent of total income=25%

Inconclusion the  percent of Jon's total income did he spend for food is 25%.

Learn more about total income here:https://brainly.com/question/842469

❗100 POINTS ❗
FOR a correct explanation of why this ain't right

I'm forced to do this 4 sb and I fr dk what HOW THIS ISNT CORRECT?!

pls help

thx​

Answers

Factors of 36 are the list of integers that we can split evenly into 36. There are overall 9 factors of 36 among which 36 is the biggest factor and its positive factors are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The Pair Factors of 36 are (1, 36), (2, 18), (3, 12), (4, 9) and (6, 6) and its Prime Factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18 and 36

Negative Factors of 36: -1, -2, -3, -4, -6, -9, -12, -18 and -36

Prime Factors of 36: 2, 3

Prime Factorization of 36: 2 × 2 × 3 × 3 = 22 × 32

Sum of Factors of 36: 91

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, factors of 36 are those numbers that exactly divide 36 leaving no remainder. In other words, we can say if two numbers are multiplied and the product is 36, then the numbers are factors of 36.

Let us do a hit and trial method to find factors of 36.

Divide 36 ÷ 2 = 18

Quotient = 18, remainder = 0

Now multiply 18 × 2 = 36

Hence, 18 and 2 are the factors of 18.

36 is a composite number as it has factors other than 1 and itself.

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 36.

The most common method we use to find factors is the prime factorization method.

In prime factorization, we express 36 as a product of its prime factors.

In the division method, we see which numbers divide 36 exactly without a remainder.

Let us calculate factors of 36 using the following two methods:

Factors of 36 by prime factorization factor tree method

Factors of 36 by upside-down division method

Prime Factorization of 36 by Upside-Down Division Method

Now as discussed above, in the prime factorization method we show factors of 36 as a product of prime factors of 36. Follow the steps to find the prime factors of 36 by the prime factorization method.

With the help of divisibility rules, find out the smallest factor of the given number. Here, 36 is an even number. So it is clearly divisible by 2. In other words, 2 divides 36 with no remainder. Therefore, 2 is the smallest prime factor of 36.

36 ÷ 2 = 18.  Now find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get a prime number as the quotient. Here, 18 is the quotient.

18 ÷ 2 = 9. Here, 9 is the quotient. Now find the prime factors of the 9.

9 ÷ 3 = 3. Here 3 is the prime number. So we can stop the process.

Prime factorization of 36 using upside-down division method is 2 × 2 × 3 × 3 = 2² × 3².

Prime Factorization of 36 by Factor Tree Method

The factor tree method is another visualization method to represent factors of 36. It also helps in determining prime factors of 36. A factor tree is not unique for a given number. Instead of expressing 36 as 2 × 18, we can express 36 as 6 × 6.

Prime factorization of 36 using factor tree method is 2 × 2 × 3 × 3 = 2² × 3².

Explore factors using illustrations and interactive examples

Factors of 33: The factors of 33 are 1, 3, 11, and 33.

Factors of 34: The factors of 34 are 1, 2, 17, and 34.

Factors of 38:  The factors of 38 are 1, 2, 19, and 38.

Factors of 30: The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.

Factors of 360: The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

Factors of 35: The factors of 35 are 1, 5, 7, and 35.

Factors of 37: The factors of 37 are 1 and 37.

Factors of 36 in Pairs

Factor pairs are the two numbers that, when multiplied, give the number 36. Find all of the factors of the number 36 using the steps below:

Step I: Start with 1 and the number itself.

Step II: Count up by ones to see if you can multiply two numbers together to get your target number.

Step III: Stop when you can’t get any more numbers in between.

Step IV: Connect the factor pairs.

Factor pairs of 36 are given below:

36 = 1 × 36

36 = 4 × 9

36 = 6 × 6

36 =12 × 3

36 = 18 × 2

Let us club the numbers in pairs.

The factors of 36 in pairs are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).

There are a total of 5 pairs of factors of 36.

We can have negative factors also for a given number.  

Since the product of two negative numbers is positive [(-) × (-) = +].

The negative pair factors of 36 are (-1, -36), (-4, -9), (-6, -6), (-12, -3), and (-18, -2)

There are a total of 5 negative pairs of factors of 36.

Important Notes:

36 is a composite number as it has factors other than 1 and itself.

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.

Pair factors of 36 are (1, 36), (4, 9), (6, 6), (12, 3), and (18, 2).

1 is a factor of every number.

Prime factorization of 36 is 2 × 2 × 3 × 3 = 2² × 3².

Challenging Questions:

Find the factors of 3600 with the help of techniques used in finding factors of 36.

Prove that the factor of a number is always less than or equal to the number itself?

Please help me answer

Answers

Answer: Second Choice

Step-by-step explanation:

What is the answer to the equation?

Answers

y=-3x+5
the slope is negative because the line is going down from left to right
the y-intercept is 5 because that’s where the line crosses the y-axis

what is the domain and range of : {(2,4) (3'6) (4,8) (5,10) (6,12)}​

Answers

Answer:

2,3,4,5,6 is the domain

4,6,8,10,12 is the range

Step-by-step explanation:

Answer:

The domain is {2,3,4,5,6} and the range is {4,6,8,10,12}.

Step-by-step explanation:

For the following equation, find a solution for the variable. Show all of your work and use complete sentences to explain the solving process that you used to find a solution for the equation. Be sure to include at least two terms from the word bank. 4+ x = 7

Answers

Answer:

x=33

Step-by-step explanation:

you move the 4 to the other side

x=7-4

so

x=3

Answer:

x=3

Step-by-step explanation:

This should be easy.

4+x=7

-4    -4

x=7-4

x=3

Word explanation:

Here, we're solving for the variable x, first, we need to isolate x and therefore subtract 4 on both sides, 7 minus 4 is 3, so x is equal to 3.

Is the sentence Equivalent or non equivalent 12:24,50:100

Answers

Answer:This sentence is EquivalentStep-by-step explanation:12:24::50:100=> 12/24 = 50/100=> 1/2 = 1/2Conclusion:

Therefore, the sentence is Equivalent.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

A watch band is 8 in long. What is its diameter when you wrap it around your wrist? Round your answer to the nearest
hundredths.
Please be accurate and explain.

Answers

Answer:

well, all you need to do is 8 x 3.14 so then you shall get your answer!

Step-by-step explanation:

11. The profit Samantha's company makes is
given by the expression 0.1(1000 + 300m)
where m is the total number of sales.
Rewrite the expression using the distributive
property. What is the profit if her company
sells 50 pieces of merchandise?

Answers

Answer: 0.1(1000 + 300m)

Use the distributive property: a x (b + c) = a x b + a x c

0.1 x 1000 + 0.1 x 300m

Evaluate both products: 100 + 30m (1)

Note: Multiplying a number by 0.1 is the same as dividing the number by 10.

We need to determine the profit when 50 pieces are sold.

Substitute m with 50 in equation (1).

100+30(50)

Evaluate product: 100 + 1500

Evaluate sum" 1600

Thus the profit is $1600.

Step-by-step explanation: I hope this helps you on any other problem! :)

Good Luck!

A plane traveled 960 miles each way to Jakarta and back. The trip there was with the wind. It took 10 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?

Answers

Answer:

Wind speed = 40 km/hr

Speed of the plane in still air = 280km/hr

Step-by-step explanation:

Formula to use

Distance = Rate multiplied by Time

D = R × T

Speed of the plane in still air = a

Speed of the wind = b

Plane with the wind (tailwind) is a + b where the time = 3hours

Plane against the wind is a - b, where the time = 4hours

This would give us 2 equations

3 × (a+ b) = 960

3a + 3b = 960 ...... Equation 1

4 × (a- b) = 960

4a - 4b = 960 ........ Equation 2

Solve this like you would with system of equations:

We solve the equation using elimination method.

Mulitply equation 1 by 4 and equation 2 by -3

4 × (3a + 3b = 960)

12a + 12b = 3840 ..... Equation 4

-3 × (4a- 4b = 960)

-12a + 12b= -2880 ........ Equation 5

Therefore we have

12a + 12b = 3840 ..... Equation 4

-12a + 12b= -2880 ........ Equation 5

24b = 960

b = 960÷ 24

b = 40

Wind Speed = 40km/hr

To find the speed of air, we use equation 2

4a - 4b = 960 ........ Equation 2

Substituting 40 which is wind of speed for b in equation 2 we would have

4a - 4(40) = 960

4a - 160 = 960

4a = 960 + 160

4a = 1120

a = 1120 ÷ 4

a = 280

The speed of the small plane in still air is 280 km/hr

URGENT PLS HELP

John is driving around town. When he reaches the gas station, he notes that he has traveled 18 miles. He reaches home 2 hours later and notes that he has traveled 34 miles. If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?

1. d = 18t + 52
2. d = 16 + 18t
3. d = 8t + 18
4. d = 8t - 18

Answers

2. d=16 + 18t because 18 represents the miles he noted and adding the 16 would be 34. Since t is representing time, and you don’t know in how much time he traveled 18 miles it’d be with the 18.

The diagonal of an isosceles trapezoid with angle to the base is equal to 30. Find the length of the height of the trapezoid if it is known that the midline of this trapezoid is equal to 8 cm.

Answers

Answer:

4.62 cm to nearest hundredth.

Step-by-step explanation:

If the parallel sides are x and y then:

x + y = 2*8 = 16

x + y = 16

If we drop a perpendicular line from one of the upper points on the trapezoid we have the height.  Let the upper point be C and the point on the base be A. Let the point on right of the base be B.

AC is the height of the trapezoid.  AB is the baseline of the triangle CAB.

In triangle CAB the angle B is 30 degrees.

As this is a 30-60-90 degree triangle

AC/AB = 1/√3 so AC = AB/ √3.

As the trapezoid is isosceles:

AB = x + 0.5(y - x)

AB = 0.5x + 0.5y

So AC = 1 /√3 (0.5x + 0.5y)

           = 1 /√3 (0.5x + 0.5(16 - x))   (Substituting for x)

            = 1 /√3 (0.5x + 8 - 0.5x)

             =8 / √3    

.              = 4.6188 cm

How do I add mixed numbers?

Answers

Step 1 - find the lowest common multiple between the denominators step 2 - multiply the numerator and denominator of each fraction step 3 - Add or subtract the numerators and keep the denominator the same.

Please look for the question in the picture.

Answers

it will be c

as

negative with negative erased together

Please look for the question in the picture.

Answers

the answer for this question is a: -9/-8

Suppose in the year 2000 the population of a country is 20 million. In the year 2010 the
population is now 24 million. If the growth of the population is exponential, approximate what the population would be in the year 2021.

Answers

Answer:

Grows by 2.4 million each year

Step-by-step explanation:

Jarad, the track star, ran the 88 yards in 10 seconds. How fast is this in miles per hour?

Answers

Answer:

18mph

Step-by-step explanation:

We convert this to solve! 1 mile equals 1760 yards,1 yard equals 3 feet, 60 seconds equals a minute, and 1 hour equals 60 minutes.

[tex]\frac{88yd}{10sec} times \frac{3ft}{1yd} times\frac{1mi}{5280ft} times\frac{60sec}{1min} times\frac{60}{1hr}[/tex]

When you multiply all that you get 18 mph

Triangle A'B'C' is a reflection of triangle ABC across line BC. Prove that ray BC is the angle bisector of angle ABA'.​

Answers

Answer is below in the picture:-

(From the problem, we know (triangle)ABC (round of equal of) (triangle)A'B'C'. So, <A'B'C' = <ABC {the properties of congruent triangles}. So, ray BC is the angle, bisector of angle ABA')

I hope it helps.

It is proved that the ray BC is the angle bisector of angle ABA'.

What are angle bisectors?

Angle bisectors are lines who bisect the considered angle. Bisect refers to splitting in two equal parts. Therefore, the bisected parts of the considered angle are half of the original angle.

When a graph is reflected along an axis, say x axis, then that leads the graph to go just in opposite side of the axis as if it in a mirror.

We will find that its symmetric, thus each point is equidistant from the axis of reflection as that of the image of that point.

From the given problem, we know Triangle A'B'C' is a reflection of triangle ABC across line BC.

Therefore, <A'B'C' = <ABC

By the properties of congruent triangles. Means if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Hence, the ray BC is the angle, bisector of angle ABA'.

Learn more about reflection here;

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Find BC.
А В
С
ош
=
=
AD = 10.5
AB = 2
СЕ = 11.5
AE = 15
BC = [?]
=

Answers

Answer:

8,5

Step-by-step explanation:

BC=AD-AB

BC=10,5-2

BC=8,5


what does the u stand for in these problems? is it the same as r?

Answers

I think "u" stands for units. [tex]u^2[/tex] means units squared which is like saying ft^2 if you were looking for the area of something with feet dimensions. So in this case, the circle has a diameter of x units (u) and an area of x units^2 ([tex]u^2\\[/tex]). It is not the same as r. "r" is most always going to be used to represent the radius.

Tom and Rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points. They let XXX represent the sum in a given turn, and they find the expected value of XXX is E(X)=17.5E(X)=17.5E, left parenthesis, X, right parenthesis, equals, 17, point, 5 points. Tom says, "A player will most likely get 17.517.517, point, 5 points in any given roll." Rosie says, "Over 100100100 turns, we can expect a total of about 175175175 points." Whose statement is correct based on the expected value?

Answers

Answer: neither statement is correct

Step-by-step explanation:

on Khan Academy

The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

What is expected value?

Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept.

According to the question

Tom and Rosie are designing a game.

In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn.  

let X represent the sum in a given turn

the expected value of X is E(X)=17.5

As

expected value is also called mean value  

i.e

highest value of sum = 6+6+6+6+6

                                   = 30

Lowest value of sum = 1+1+1+1+1

                                   = 5

Therefore,

Mean = [tex]\frac{30+5}{2}[/tex]

          = 17.5

Now,

Tom says, "A player will most likely get 17.5

This statement is correct as per expected value which is mean value and it is 17.5 .

Rosie says, "Over 100 turns, we can expect a total of about 175

This statement is incorrect as per expected value as

expected value = 17.5

when 100 turn will happen it will

17.5 * 100

= 1750

Hence, The statement by Tom "A player will most likely get 17.5 " is correct based on expected value .

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A child's height increased from 21 to 32 inches. What was the percent increase in the child's height

Answers

Answer:

52.4

Step-by-step explanation:

% change = 100 x final initial/initial

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